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Fullerenes refer to a class of specially engineered carbon-atom closed structures (typically shaped like a football) in nanotechnology. This is a subject that falls into Materials Science. I happened to have edited some Chemistry texts on it years ago.
Because “fullerene" does not refer to just one type of carbon molecule, but a whole class of different masses and sizes, you may want to decide wether the context requires the use of "フラーレンの" (referring to generic characteristics) or “フラーレン状の” (referring specifically to geometric characteristics).
Note: graphitic ("like graphite") and amorphous ("without specific strcutural pattern") are also terms used to describe the shape of carbon atoms. The other two terms are tetrahedral (diamond) and here fullerenic.
I appreciate both of your answers which clarified my questions. It's about the specific "shape" of a soot particle in comparison with "graphitic" and "amorphous", in which sense I assumed フラーレン状 would better fit as a heading. Your links were intersting enough to know why the term has been in use. Thank you very much. - 4 KudoZ points were awarded for this answer